Newest New Yorkers - Characteristics of the City's Foreign-Born Population (published in 2013).
You can find more recent data by neighborhood and or CD in the other resources on this Guide, just search by foreign-born population.
The US Census' Database American FactFinder - access to data about the US from several censuses and surveys.
Here's an additional list of Data Resources and Tools from the US Census Bureau
Check out this PPT from the Census staff called How to Use American Community Survey (ACS) Geodatabase Files and ArcMap
For help, contact the US Census' Data Dissemination Branch at: firstname.lastname@example.org, 301-763-2032